相关论文: Kirkman's hypothesis revisited

We prove an analogue of the Lagrange Inversion Theorem for Dirichlet series. The proof is based on studying properties of Dirichlet convolution polynomials, which are analogues of convolution polynomials introduced by Knuth in [4].

We present a simple inductive proof of the Lagrange Inversion Formula.

We propose a detailed proof of the fact that the inverse of Ackermann function is computable in linear time.

We present a proof of Hadamard Inverse Function Theorem by the methods of Variational Analysis, adapting an idea of I. Ekeland and E. Sere.

We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.

We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.

We show that Pinney's equation [2] with a constant coefficient can be reduced to its linear part by a simple change of variables. Also, Pinney's original solution is simplified slightly.

We prove Burkholder inequality using Bregman divergence.

We derive a version of Lagrange's mean value theorem for quantum calculus. We disprove a version of Ostrowski inequality for quantum calculus appearing in the literature. We derive a correct statement and prove that our new inequality is…

This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.

The Riemann hypothesis is proved by quantum-extending the zeta Riemann function to a quantum mapping between quantum $1$-spheres with quantum algebra $A=\mathbb{C}$, in the sense of A. Pr\'astaro \cite{PRAS01, PRAS02}. Algebraic topologic…

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…

We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related…

The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…

In this paper we consider some possible approaches to the proof of the Riemann Hypothesis using the Li criterion.

A proposed solution to the Riemann Hypothesis

We introduce an inhomogeneous variant of Kaufman's measure, with applications to diophantine approximation. In particular, we make progress towards a problem related to Littlewood's conjecture.

In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell…